`cos(sin^(-1)x)=sqrt((1-x^(2)))`

If agt0 and A=int_(0)^(a)cos^(-1)xdx, and int_(-a)^(a)(cos^(-1)x-sin^(-1)sqrt(1-x^(2)))dx=pia-lamdaA . Then lamda is

The value of int_(-a)^a(cos^(- 1)x-sin^(- 1)sqrt(1-x^2))dx is (a>0) there int_0^acos^(- 1)x dx=A) is

Sove 2 cos^(-1) x = sin^(-1) (2 x sqrt(1 - x^(2)))

Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) cos"[tan^(-1){"sin"(cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) cos [tan^(-1) (cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

Prove that : sin^(-1) ""(x)/(sqrt(1 + x^(2))) + cos ^(-1) "" (x + 1)/( sqrt( x^(2) + 2x + 2)) = tan^(-1) ( x^(2) + x + 1)

Find the domain of the following following functions: (a) f(x)=(sin^(-1))/(x) (b) f(x)=sin^(-1)(|x-1|-2) (c ) f(x)=cos^(-1)(1+3x+2x^(2)) (d ) f(x)=(sin^(-1)(x-3))/(sqrt(9-x^(2))) (e ) f(x)="cos"^(-1)((6-3x)/(4))+"cosec"^(-1)((x-1)/(2)) (f) f(x)=sqrt("sec"^(-1)((2-|x|)/(4)))

Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2) + 2))

Prove the following: "cos"{tan^(-1){sin(cot^(-1)x)}}= sqrt((1+x^2)/(2+x^2))